Numerical Simulation of a Dam Break Flow Using Finite Volume Approach

Abstract

The fluid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation were used as the governing equations. A program is developed to solve highly deformed free surface problems common in waves formed during wave propagation, which transforms the run up model from the physical domain to a computational domain with McCormack scheme & finite volume modeling technique. A simple and accurate projection of finite volume method is developed for solving shallow water equations in two space dimensions. The aim of such a method compared to the conventional finite volume methods is to solve shallow water equations efficiently and with an appropriate level of accuracy.

The computation of governing equations (both momentum equation and continuity equations) to be solved are generally called the Saint-Venant equations. These equations are highly nonlinear partial differential equations, the solutions of which are very much complex. Numerical approaches are generally employed to solve these equations and proper discretization with proper selection of grid size and time step provides the results more effectively and accurately. In the present research work the Saint–Venant equations are solved through the Maccormack explicit finite volume scheme. Conversion of governing equations into ordinary partial differential equation forms and the simple discretization of this equation by explicit scheme using CFD tool are presented in this paper. Matlab as the computing tool and suitable program has been performed successfully. The water surface elevation and velocity of the shallow water wave are found through this numerical model. The numerical model is verified using results from ANSYS for a channel.

Finally all computed results are shown in5terms of tables and plots. This paper investigates dam-break flow problem with the aim to capture fluid flow in transition to solve one dimensional shallow-water equations (SWE). Applying compact MacCormack type schemes with high accuracy approach, governing equations are solved using explicit scheme. Parameters for one-dimensional flow problem with respect to water depth and velocity.